Trajectory Clustering Aided Personalized Driver Intention ...

IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. X, NO. X, MONTH YEAR

Trajectory Clustering Aided Personalized DriverIntention Prediction for Intelligent Vehicles

Dewei Yi, Jinya Su∗, Cunjia Liu, Member, IEEE and Wen-Hua Chen, Fellow, IEEE

Abstract—Early driver intention prediction plays a sig-nificant role in intelligent vehicles. Drivers exhibit vari-ous driving characteristics impairing the performance ofconventional algorithms using all drivers’ data indiscrimi-natingly. This paper develops a personalized driver inten-tion prediction system at unsignalized T-intersections byseamlessly integrating clustering and classification. Poly-nomial regression mixture (PRM) clustering and Akaike’sInformation Criterion are applied to individual drivers tra-jectories for learning in-depth driving behaviours. Thenvarious classifiers are evaluated to link low-level vehiclestates to high-level driving behaviours. CART classifierwith Bayesian optimization excels others in accuracy andcomputation. The proposed system is validated by a real-world driving dataset. Comparative experimental resultsindicate that PRM clustering can discover more in-depthdriving behaviours than manually defined manoeuvres dueto its fine ability in accounting for both spatial and tempo-ral information; the proposed framework integrating PRMclustering and CART classification provides promising in-tention prediction performance and is adaptive to differentdrivers.

Index Terms—Intelligent vehicle; Driver behaviour pre-diction; Polynomial regression mixture; Trajectory cluster-ing.

I. INTRODUCTION

Recent advancements of Artificial Intelligence (AI) havestimulated the rapid development of industrial informaticsapplications, especially in intelligent vehicles for smart cities[1–3]. In particular, machine learning with big data has madea great progress in perception and decision making enhancingdriving safety, convenience and fuel-efficiency for intelligentvehicles [4–7]. A number of advanced driver assistance sys-tems (ADAS), e.g. adaptive cruise control and lane departurewarning, have been developed to augment drivers’ situationawareness accuracy and enhance decision making capabilitiesby perceiving the environmental situation in real time, alertingdrivers to potential dangers, or even taking over certain drivingtasks in urgent situations. Despite all the effort and progressachieved so far, there is still long way to go to deploy driver

Manuscript received May 21, 2018; revised August 10, 2018; ac-cepted December 18, 2018. This work is jointly supported by the U.K.Engineering and Physical Sciences Research Council (EPSRC) Au-tonomous and Intelligent Systems programme under the grant numberEP/J011525/1 with BAE Systems as the leading industrial partner.Dewei Yi would also like to thank Chinese Scholarship Council forsupporting his study in the UK.The authors are all with the Department of Aeronautical and AutomotiveEngineering, Loughborough University, Loughborough LE11 3TU, U.K.E-mail: [email protected] (Dewei Yi); [email protected](Jinya Su∗ corresponding author); [email protected] (CunjiaLiu); [email protected] (Wen-Hua Chen).

assistance system robustly and effectively in realistic trafficenvironment to prevent majority of accidents.

In particular, critical challenges still remain in negotiatingtraffic intersection safely in urban areas. This is because ma-noeuvring through interactions is a stressful task due to multi-ple directions of movements along with the need to maximallyaccount for other drivers’ possible errors [8]. According tothe EU community road accident database CARE, intersectionrelated fatalities accounts for more than 20% in the EU duringthe last decade (2001-2010) [9]. This is also the case in theUnited States, where an estimated 45% of injury crashes and22% of roadway fatalities in the U.S. are intersection related[10]. It is also reported that in these accidents driver’s inabilityto correctly assess and/or observe the danger involved in suchsituations [11] is a main contributing factor.

In the past decade, a number of research and developmentefforts have been devoted to intersection decision supportsystems. For example, in [12] the problem of whether adriver will stop safely or not given the traffic signal indica-tion (i.e. compliant or violating behaviours) was considered,where the binary classification problem was solved usingdiscriminative Support Vector Machine (SVM) and generativeHidden Markov models (HMM) respectively based on threekey features including range to intersection, speed and longi-tudinal acceleration. In [13, 14], driver’s turning behaviourrecognition at T-intersection (e.g. straight driving, left orright turn) was investigated using discriminant analysis andlong short term memory based Recurrent Neural Network(RNN) respectively, where position, heading and velocity werechosen as features. In [15], a Bayesian network is drawn toaddress the turning intent prediction at arbitrary intersectionsby incorporating knowledge about the intersection layoutusing contextual information extracted from a digital map. Inaddition to academic research efforts, various projects havealso been seen in automotive sector. For example, in Europe,the InterSafe project was created by the European Commissionto increase safety at road intersections [16]. In the U.S., theIntersection Decision Support project [11] and the CooperativeIntersection Collision Avoidance System project [17] weresponsored by the Department of Transportation (DOT) anduniversities to develop intersection collision avoidance systemsand its demonstration.

In contrast to the majority of preceding works where ageneric (or average) system for all drivers is built by treat-ing individual drivers’ data indiscriminately [18], we aimto develop a personalized system dedicated to intersectionassistance. This is done by observing that different drivershave distinct driving preferences and characteristics even for

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the same manoeuvres at intersections. For example, for amultiple lane, some drivers may prefer to drive in the innerlane while others prefer outer lane. Even for a single lane,an aggressive driver may exhibit distinct turning patterns incomparison to a mild one. To make the system better cooperatewith individual drivers, the personalized driving characteristicsshould be accommodated in driving behaviour recognition sothat the so-called “adaptive aiding” [1, 19] can be provided tothe drivers at the right time and in a proper manner.

To effectively accommodate driving characteristics, the per-sonalized driving data of individual drivers is exploited includ-ing high-level trajectories and low-level vehicle states such asvelocity and heading. The proposed driver behaviour predic-tion system comprises two layers including offline behaviourlearning via high-level trajectories and online behaviour pre-diction via low-level vehicle states. In the offline stage, dif-ferent from existing work [20] where classifiers are trained bylabelled data. The proposed system comprises two steps. First,driving behaviours are automatically learnt by dividing thetrajectories of a particular driver into various categories usingclustering algorithms, where the cluster number is optimizedusing the classical Akaike’s Information Criterion (AIC) [21].This clustering-aided approach, in contrast to conventionalones where only a set of manually defined manoeuvres areconsidered [14], automatically learns the driver behavioursusing a purely unsupervised data-driven approach. Owing tothis step, the proposed behaviour prediction system is adaptiveto different drivers and arbitrary road intersections withoutmanually labelling the historical data. Secondly, based on thelearnt driving behaviours represented by different clusters,low-level vehicle state data including velocity and headingin each cluster are drawn to build a mapping between low-level sensing data and high-level driving behaviours usingthe classical Classification and Regression Trees (CART)algorithm. Then, in the stage of online prediction with theadvent of new sensing data, the trained CART is drawn topredict individual drivers’ behaviour represented by differentclusters.

To the best of the authors’ knowledge, this work is the firstattempt to integrate trajectory clustering and behaviour clas-sifier to solve the problem of personalized driving behaviourprediction, particularly the proposed framework is validatedby using a recently collected dataset from real-world drivingexperiments with promising performance. More precisely, themain contributions are summarized.• Trajectory clustering is adopted to learn individual drivers’

behaviours from history trajectories resulting in a num-ber of in-depth manoeuvres/behaviours without manuallylabelling. Owning to this step, the proposed behaviourprediction system is adaptive to different drivers and variousintersection layouts automatically;

• Various classifiers for driving behaviour prediction are com-pared to identify a suitable one for the proposed framework,where CART classifier with Bayesian hyperparameter opti-mization outperforms others.

II. DRIVER BEHAVIOUR PREDICTION

In order to achieve personalized driver behaviour prediction,two key problems should be addressed. The first one is how toautomatically label personal trajectory data, since manual datalabelling is painful and inefficient. Another is how to build therelationship between driving features and driver behaviours. Toovercome the first problem, trajectory clustering is adoptedto discover the in-depth behaviours for individual driversin an automatic manner. To deal with the second problem,supervised learning is applied to predict driver behaviours byusing vehicle related measurements.

In this work, the information on driving behaviour is mainlygrouped into two levels including “high-level trajectories” and“low-level driving features”. In particular, “low-level drivingfeatures” denote information related to vehicle dynamics (e.g.speed and heading, which are only functions of time), rep-resenting short-term (or instantaneous) driving behaviours [7].While “high-level trajectories” denote vehicle trajectories (i.e.spatial-temporal process, which are essentially functions ofboth position and time) reflecting drivers’ long-term behaviourinformation (e.g. driving preference, turning pattern).

In the proposed system, “high-level history trajectories” areinputs of clustering algorithm for offline learning which canautomatically learn drivers’ in-depth behaviours (e.g. drivingpreference, turning pattern). While “low-level driving fea-tures” are inputs of classification algorithm, which can predictdriver behaviours in real-time. In the remaining part of thissection, the proposed personalized driver behaviour predictionsystem aided by trajectory clustering is briefly discussed,where its overall diagram is shown in Fig 1 including offlinedriving behaviour learning and classifier construction, andonline behaviour prediction.

High-level Trajectories

PRM clustering

Offline: behaviour learning and mapping

Clusters Behaviour categories

CART classifier

Manoeuvre

Online: behaviour prediction

one Adaptive aiding

Sensing data

Clusters CART

TrainingLow-level

Driving features

Fig. 1. Diagram of trajectory clustering aided personalized driver be-haviour prediction system: blocks in red are for offline behaviour learningand mapping construction, blocks in light blue are for online behaviourprediction.

In the offline training layer, “high-level history trajectories”of individual drivers are divided into different categoriesrepresenting various driving behaviours (e.g. straight driving,mild turn, aggressive turn) by using clustering algorithm. Thetrajectory clustering algorithm in this work can consider spatialand temporal information simultaneously. At the same time,the clustering approach is adaptive to different drivers and anyintersection layouts (e.g. T-junction, crossroad). Consideringthat the length of trajectories is variable, PRM clusteringalgorithm is adopted which is independent of trajectory length


by using regression analysis with expectation maximisation(EM) algorithm for parameter learning. Trajectory clusteringis to implement auto-tagging of driving behaviours and adaptsto each individual driver. Then, CART classification modelsare trained to classify different driving behaviours by treatinglow-level vehicle states as the features (e.g. speed, heading).In the online execution layer, observed vehicle state data areclassified into different clusters using the trained CART model,where each cluster represents a particular driving behaviour.Based on the proposed framework, the driving behavioursof individual drivers can be understood by the vehicle andconsequently “adaptive aiding” can be provided to the driverat the right time and in a proper manner [1]. In the followingsections, each element of the framework is elaborated.

III. CLUSTERING FOR BEHAVIOUR LEARNING

In this section, offline behaviour learning is detailed forindividual drivers for the purpose of personalized behaviourlearning. As highlighted in Section I, different from theexisting works where drivers’ behaviours at intersection aremanually defined by a number of given manoeuvres, e.g.continuing straight, turning right or left, this work relies onclustering algorithms to automatically learn driver behavioursby analysing the high-level history trajectory data of individualdrivers. As a result, this approach is adaptive to differentdrivers and arbitrary road intersection layouts.

Clustering is an efficient way to discover hidden patternsin the dataset by an unsupervised manner. Various clusteringalgorithms are available, each of which has its own prosand cons [22, 23]. For instance, centre-based approachessuch as k-means clustering are simple but cannot directlyhandle trajectories with various lengths. While approachessuch as Gaussian mixtures cannot tackle trajectories measuredat different time points or that contain missing observations.As a consequence, trajectories with the same spatial patternbut in opposite directions (or trajectories with similar spatialpattern but with different velocities) may be misclassified intoone cluster [24]. Therefore, it is necessary to consider thecharacteristics of trajectory clustering problem in selecting anappropriate algorithm. In comparison with common clusteringproblems, trajectory clustering has its own characteristicssummarized as follows: (a) trajectories usually have differentlengths due to their different time durations in the region ofinterest; (b) each trajectory is a spatial-temporal process sinceit is essentially a function of both position and time. As aresult, two trajectories with similar spatial pattern may havedistinct temporal pattern and so should not be categorized intoone cluster.

Considering the aforementioned characteristics, PRM clus-tering is adopted, which can effectively handle the clusteringproblem with variable lengths while simultaneously takingspatial and temporal information into account [24]. In addi-tion, to determine the “optimal” cluster number, the classicalAkaike’s Information Criterion (AIC) [21] is adopted. In thefollowing subsections, some pivotal elements of the trajectoryclustering are elaborated.

A. Polynomial Regression Mixture (PRM)PRM divides vehicle historical trajectories of a specific

driver into different clusters by minimizing the differencesbetween data and regression models. Let Y = {y1, . . . , yn} bea set of the driver’s vehicle historical trajectories containingn trajectories, where each trajectory yi (i = 1, 2, ..., n) is asequence of position measurements with length ni observedat a set of time indexes xi (in this work, trajectories representhistorical movement of a driver at unsignalized T-junctions).The conditional probabilistic model for cluster k (each clusterrepresents a category of driving behaviour) is represented bypk(yi|xi, θk). Therefore, Probability Density Functions (PDFs)of all clusters (i.e. all driving behaviours) can be given by

p(yi|xi,Θ) =

K∑k=1

αkpk(yi|xi, θk), (1)

where Θ is the set of θk and αk (Θ = {θk, αk}). θkrepresents parameters of k-th model (driving behaviour) andαk represents the probability that the i-th trajectory is assignedto cluster k (driving behaviour k) satisfying

∑Kk=1 αk = 1

with K being the number of clusters.1) Definition of polynomial model: A trajectory within a

cluster can be treated as the mean trajectory of the clusteradded a noise and the mean trajectory of a cluster can beobtained by (1). Therefore, it is assumed that a trajectoryyi can be represented by a p-th order polynomial regressionperturbed by a Gaussian error when xi is given. The regressionof yi on xi is given by

yi = Xiβ + εi, (2)

where εi ∼ N(0, σ2I) is the Gaussian error, Xi is a ni×(p+1)regression matrix, and β is regression coefficients which is a(p+ 1)-vector. The p-th order regression matrix Xi evaluatedat xi is given by

Xi =

1 xi1 x2i1 . . . xpi1

......

... . . ....

1 xinix2ini

. . . xpini

.For different trajectories, the row number of Xi is different

to be adaptive to different trajectory lengths. The columnnumber of Xi is the same when the order p of polynomialregression is determined. This step is to transfer a trajectoryinto a regression form. The regression model (2) defines theconditional PDF of yi given xi as N (yi|Xiβ, σ

2I). Integrating(2) into the mixture density (1) by incorporating dependenceof this PDF on k, represented by {βk, σ2

k}, results in thefollowing PRM

p(yi|xi,Θ) =

K∑k=1

αkN (yi|Xiβk, σ2kI). (3)

The log-likelihood of trajectories set Y is computed bysumming up the conditional probability density of all ntrajectories, given by

log p(Y |X,Θ) =

n∑i=1

log

K∑k=1

αkN (yi|Xiβk, σ2kI), (4)


where X = {X1, · · · , Xn} denote the set of known regressionmatrices, Θ represents all unknown parameters {βk, σ2

k, αk}.(4) is used in EM algorithm to derive the model parametersbased on maximum likelihood estimation.

2) EM for parameter optimization: zi is the cluster mem-bership for trajectory yi, then the joint density of yi and zican be given by

p(yi, zi|xi) = αzipzi(yi|xi) = αziN (yi|Xiβzi , σ2ziI). (5)

The overall log-likelihood function L can be obtained bysumming up all n trajectories’ log joint density, given by

L =

n∑i=1

logαziN (yi|Xiβzi , σ2ziI). (6)

E-step: Since cluster memberships zi are unobservable, pos-terior p(zi|yi,xi) is used in the E-step. The membershipprobability p(zi|yi,xi) that the i-th trajectory was generatedfrom cluster zi is calculated by

wik = p(zi = k|yi,xi) ∝ αkpk(yi|xi) = αkN (yi|Xiβk, σ2kI).

The posterior expectation of L in (6) is computed with respectto the above posterior, given by

E[L|yi,xi] =

n∑i=1

K∑k=1

wik logαkN (yi|Xiβk, σ2kI). (7)

M-step: In the M-step, (7) is maximized with respect to theparameters Θ = {βk, σ2

k, αk}, where the solution is given by

βk = [∑ni=1 wikX

Ti Xi]

−1∑ni=1 wikX

Ti yi, (8)

σ2k =

∑ni=1 wik||yi−Xiβk||2∑n

i=1 wik, (9)

αk = 1n

∑ni=1 wik. (10)

Remark 1: The computational complexity of EM algorithm islinear in the number of trajectories. In the initialization phase,the membership probabilities are randomly sampled and thenthe M-step is started. E-step and M-step will be repeated untila local maximum of log-likelihood is reached. However, inpractice, convergence is usually detected when the incrementalimprovement ratio of log-likelihood drops below a threshold.

B. Optimal cluster numberIt is usually challenging to determine the “optimal” cluster

number k∗ for PRM. In this work, k∗ is derived using Akaike’sInformation Criterion (AIC) [21], which is an effective mea-sure for assessing clustering model quality. According toAkaike’s theory, the most appropriate model has the smallestAIC value, where AIC is defined by

AIC = N ∗ log(det( 1N

∑N1 ε(t, θN )(ε(t, θN ))T ))

+ 2np +N ∗ (ny ∗ (log(2π) + 1)),(11)

where N is the number of samples, ε(t) is a ny-by-1 vectorof prediction errors with ny the number of model outputs, θNis the estimated parameters with np being its number. Afterobtaining clustering configuration via PRM with differentcluster numbers, one can calculate the corresponding AIC

values, where the cluster number k∗ corresponding to thesmallest AIC value is selected for each driver.

AIC is usually adopted to determine “optimal” clusternumber for clustering problems where data has the samedimension [25]. In this work, vehicle trajectories in variousclustering configuration are generally with variable lengths andtherefore AIC value for each clustering configuration cannotbe directly calculated. To solve the problem, trajectories ofvariable lengths are transferred into a fixed number of param-eters using regression analysis. Considering the characteristicsof vehicle motion at T-intersection, the constant accelerationmodel is adopted in x and y direction respectively, whichcorresponds to a polynomial of order 2

x(t) = x0 + vx0t+ 12axt

2, y(t) = y0 + vy0t+ 12ayt

2

where x(t), y(t) denote the longitudinal and latitudinal move-ment with x0, vx0, ax and y0, vy0, ay representing the initialposition, velocity and acceleration in x and y directions. Afterfitting trajectories using polynomials of order 2, each trajectorycan be represented by six coefficients x0, vx0, ax, y0, vy0 anday . As a result, AIC values can be calculated under differentclustering configuration easily.

In practice, however, the range of different coefficients mayvary a lot due to different physical meanings, consequently, Z-score [26] is adopted to normalize the coefficients. In compar-ison with other normalization approaches, Z-score can retainthe shape properties of the original data such as skewness andkurtosis. For a vector x, Z-score is defined by z = x−x

σ , wherex and σ denote the mean and standard derivation of vector xrespectively. The main steps for the optimized PRM clusteringare summarised in Algorithm 1.

Algorithm 1: Steps for PRM with optimised cluster number.1. Given a user-defined maximum cluster number kmax;2. Perform a series of PRM clustering under i =

1, · · · , kmax resulting in PRM(1), · · · , PRM(kmax);3. Calculate AIC value for each clustering configuration us-

ing formula (11) resulting in AIC(1), · · · , AIC(kmax);4. Optimal cluster number k∗ is determined by k∗ =

argkmax

mini=1

AIC(i), where PRM(k∗) denotes the optimalclustering configuration.

IV. CLASSIFICATION FOR BEHAVIOUR PREDICTION

In Section III, high-level driving trajectories are automat-ically divided into different categories using trajectory clus-tering algorithm, where each trajectory category representsone kind of driver behaviour. The next step is to use low-level vehicle state to predict the driver behaviour for real timeapplications. With the rapid development of sensing technolo-gies, nowadays it is very easy to assess various vehicle statedata characterising various manoeuvres and driving patterns.In this paper, vehicle speed and heading are chosen as thefeatures due to the following main reasons: (i) these measuresare non-intrusive and easily accessible via IMU and GPSsensors, and have a lower requirement on working condition


in comparison with other approaches such as computer visionbased ones; (ii) these features have been proved to be effectivein characterising driving behaviours [13]. For instance, a driverturning across traffic usually slows down and at the same timesteers the vehicle in an appropriate direction.

After features are defined, the driver behaviour predictionis then formulated as a classification problem building animplicit mapping between vehicle state measurements andtrajectory clusters. In real time applications with the adventof new sensing measurements, the trajectory cluster represent-ing various driving behaviours can be predicted. In machinelearning applications, it is generally not easy to select anappropriate algorithm for the task of interest. Consequently,different classifiers are first compared so that the most suitableone is identified.

A. Classifier selection

Classifier selection is generally based on problem charac-teristics, personal experience and experimental comparison. Inthis work, classifier is adopted to predict driving behaviour inreal time so that suitable follow-up driving assistance can beprovided to the driver. In addition, the classifier should also besimple and easy to certify by industry (e.g. white box model).A number of classification algorithms are implemented andcompared in this work, which include Discriminant Analysis(DA) [27], Classification and Regression Tree (CART) [28],Naive Bayes (NB) [29] and Support Vector Machine (SVM)[30] and their variants. According to the problem character-istics and experimental results in Section V-E, CART withBayesian parameter optimization [31] outperforms others sig-nificantly and therefore is adopted in the proposed framework.For the sake of completeness, the CART algorithm is brieflyintroduced in the following subsection.

B. Classification And Regression Tree (CART)

CART is a popular non-parametric statistical classifier,which can identify mutually exclusive and exhaustive sub-groups of a population whose members share certain commoncharacteristics that affect the dependent variable of interest.In this approach, the data space is recursively partitioned intosmaller partitions using binary splitting according to certainsplitting rules (for node and threshold selection) until certainstopping rules are reached. Then a simple predictive model isfitted within each partition. CART implicitly performs variablescreening, i.e. selecting the most discriminatory features atthe top parts of decision tree. Therefore, it can obtain bet-ter performance for the driver behaviour prediction in thiswork, where features (i.e. speed and heading) and labels (i.e.behaviour categories) have strong corrections. In addition,in comparison to other algorithms (e.g. DA), CART doesnot require any assumptions of linearity or data distribution.Due to its fine properties such as a simple structure, lowcomputation load and easy to interpret, this approach hasfound wide applications [32, 33]. The detailed algorithm isreferred to [32] due to a lack of space, where the pseudocodesare given as follows for the sake of completeness.

Algorithm 2: Classification And Regression Tree (CART)model

1. Given a sequence of examples S and a set of discreteattributes A;

2. For each attribute ai ∈ A, the set of attribute values Ai

is partitioned into two disjoint subsets AiL and AiR, letXi denote all possible AiL;

3. For each AiL ∈ Xi, calculate the Gini gain/Mean SquaredError (MSE) and select the variable (AiL,q = AiL) whichmaximizes Gini gain or minimizes MSE (AiL,q is a spilt);

4. Send data S(AiL,q) to the “leaf node” and S(AiR,q) tothe “right node”;

5. Recursively repeat the same process on these two“nodes” until stopping rules are satisfied;

6. Return the CART model.

Remark 2: There are generally certain stopping rules in CARTto avoid its adverse effects such as overfitting. In this paper,one of the stopping rules is considered, i.e., the minimum leafsize. A smaller leaf size may make the model more prone tocapturing noise in training data. In this work, the determinationof minimum leaf size is transformed into the minimizationof the cross validation loss for CART, which is solved usingBayesian optimization [31, 34] (see, Section V-C).

V. EXPERIMENTAL VALIDATION

In this section, experimental validation is conducted onthe proposed framework for driver behaviour prediction atT-intersection. The experiments contain clustering for offlinedriver behaviour learning and online driver behaviour predic-tion. All aforementioned elements of the proposed system arevalidated by using the naturalistic real-world IVSSG datasetdetailed in Section V-A. In the offline phase, the determinationof optimal cluster number for individual drivers is investigatedin Section. V-B. This is to discover in-depth driving behavioursso that the system is adaptive to individual drivers. Moreover,CART parameters are optimized by Bayesian optimization inSection. V-C. In addition, resubstitution and k-fold cross val-idation methods are used to evaluate prediction performance.The procedure of resubstitution and k-fold cross validationare explained in Section. V-D and prediction performance ispresented in Section. V-E. It is also noted that all algorithms inthis paper are implemented in Matlab 2017a under Windows7 Operation System and are evaluated on a PC with thefollowing configuration: Intel Core i5-CPU at 3.20 GHz with16 GB of RAM.

A. Naturalistic Driving DatasetThe Intelligent Vehicle and Safety System Group (IVSSG)

dataset was collected on public roads near the AustralianCentre for Field Robotics (ACFR) at the University of Sydney[13], where the field of interest (FoI) is a T-intersection. Duringthe experiments, three participants are guided to performapproximately 10 passes in 6 possible manoeuvres such asdriving straight across the top of the interaction, turning intoand the intersection left or right. During the data collection,drivers conducted different manoeuvres following their own


habits and driving characteristics. The spatial plots of datacollected around the intersection for three participants areshown in Fig 3. In the experiments, global navigation satellitesystem (GNSS) was used to record vehicle position at afrequency of 10 Hz. In addition, a strap-down IMU wasadopted to collect vehicle inertial data, while vehicle’s wheelencoders provided speed information. The frequency for bothinertial data and speed is 100 Hz. Moreover, in the dataset,an extended Kalman filter has been adopted to fuse andfilter the raw data, where the filtered vehicle state estimateswere available at a rate of 100 Hz [13]. Once the data wascollected, a bounding box was created around the intersectionto define the FoI (i.e. the area only containing manoeuvrestraversing the intersection of interest). The test duration, thenumber of trajectories and the number of observations fordifferent drivers are displayed in Table I. Moreover, the IVSSGdataset adopted in this work has been made open access andcan be accessed via its.acfr.usyd.edu.au/datasets/naturalistic-intersection-driving-dataset.

TABLE ISUMMARY OF DATASET

Participant No. Test Duration No. of Trajectory No. of ObservationDriver1 74 mins 69 106616Driver2 100 mins 71 152971Driver3 51 mins 73 114456

B. Behaviour learning via PRM clusteringThe first step of offline training is trajectory clustering

for driving behaviour learning. In this work, PRM discussedin Section III is drawn to divide driving trajectories intodifferent categories representing various driving behavioursfor individual drivers. Different parameters should be speci-fied in this approach such as polynomial order, threshold ofimprovement ratio in EM algorithm and cluster number. Inthis work, the polynomial order is chosen to be 2. This isbecause driving through a T-intersection can be representedby the constant acceleration model. Moreover, the thresholdof improvement ratio for parameter optimization is chosen1 × 10−6 following the setting in [24]. While the optimalcluster number is determined using AIC value as discussedin Section III-B.

Considering that the T-intersection under consideration con-tains various manoeuvres, the cluster number for AIC valuecalculation ranges from 1 to 15 to accommodate variousdriving patterns in the same manoeuvre and abnormal drivingtrajectories. The AIC values under different cluster configu-rations for all three participants are displayed in Fig 2. Itcan be seen that the “optimal” cluster numbers accordingto AIC values are 10, 10 and 9, respectively. Under thisparameter setting, the clustering results for three participantsare displayed in Fig 3, where each colour represents one typeof trajectory category. Bold colour line of clusters in longitudeand latitude in Fig 3 indicates the mean trajectories of differentclusters.

It follows from Fig. 3 that: (1) although there are only sixdifferent manoeuvres at T-intersection, more than six typesof driving behaviours are learnt using the data-driven PRM

1 2 3 4 5 6 7 8 9 10 11 12 13 14 150

500

1000

1500

2000

2500

3000

AIC

Driver1Driver2Driver3

Fig. 2. AIC Values under different cluster number k for different drivers.

clustering; (2) for different drivers, the number of drivingbehaviours may be different due to their personalized driv-ing characteristics; (3) PRM clustering accounting for bothspatial and temporal information can discover more in-depthbehaviours than manually defined manoeuvres. Trajectories ina specific manoeuvres display significantly different temporalpattern (see, right column in Fig. 3). For instance, in Fig. 3–(c) and Fig. 3–(d), trajectories within cluster 4 and cluster8 of driver 2 are the driving passes from south-east to north-east while their speeds are different. More specifically, turningspeed of cluster 4 is faster than cluster 8. Different frommanually defined manoeuvres focusing on spatial information,the proposed system considers both spatial and temporalinformation when defining manoeuvres. Therefore, trajectorieswithin cluster 4 and cluster are divided into two differentclusters rather than one;Remark 3: With a large amount of driving trajectories forindividual drivers, the PRM clustering can also be adopted todiscover abnormal driving. Without clustering analysis, it ischallenging to define abnormal driving in trajectory big data.

C. Optimized CART classifier

The CART algorithm for driving behaviour classificationis further discussed in this section. Generally speaking, thedepth of a tree can be controlled by Min Leaf Size (MLS)and Min Parent Size (MPS), where MLS determines theminimum number of observation per leaf and MPS determinesthe minimum number of observation per branch node. Inthis work, these parameters are optimized by minimizing theclassification loss using Bayesian optimization. In Bayesianoptimization, certain stopping rules exist such as maximumnumber of iterations and maximum running time. Consideringthat the optimization process occurs in offline learning and sothe running time is not the main concern, only the maximumnumber of iterations is considered, which is chosen 30. Thevalue of MLS is searched among log-scaled in the range of[1,max(2, n−1)], where n is the number of observations. AndMPS is determined by

MPS = max[M, 2×MLS],

http://its.acfr.usyd.edu.au/datasets/naturalistic-intersection-driving-dataset/

http://its.acfr.usyd.edu.au/datasets/naturalistic-intersection-driving-dataset/


(a) Driver1: Trajectory clustering in FoI (b) Driver1: Clusters in longitude and latitude

(c) Driver2: Trajectory clustering in FoI (d) Driver2: Clusters in longitude and latitude

(e) Driver3: Trajectory clustering in FoI (f) Driver3: Clusters in longitude and latitude

Fig. 3. Each row is the results for a driver: left column is the trajectory clustering results; right column is the trajectory clustering results in longitudeand latitude and bold colour lines are mean trajectories of clusters.

where M is a fixed number in CART model, which is 10 in thispaper. Under this parameter setting, the relationship betweenthe estimated objective function values and various minimumleaf sizes for driver1 are shown in Fig 4.

It follows from the figure that the optimal minimum leafsize is 15.

D. Resubstitution and k-Fold Cross Validation

In this paper, two of the most popular metrics are used todemonstrate algorithm performance named the resubstitutionerror [35] and the k-fold cross validation error [36]. Inparticular, the resubstitution error is derived from trainingdata, where a lower resubstitution error means a better fitness

for given data and results in a better accuracy. However, theresubstitution error is for training data and may lead to theproblem of overfitting. Therefore, the cross validation erroris also considered. In k-Fold Cross Validation, the originaldataset is randomly divided into k subsets of equal size andhold-out method is repeated by k times. For each time, oneof the kth subsets is retained for testing (i.e. testing set), andthe remaining (k − 1) subsets (i.e. training set) are used fortraining. As a result, every data point appears in a test setonly once and appears in training set (k− 1) times. The finalk-fold cross validation error is the average of errors of eachfold. The variance of the resulting estimate is reduced with anincrement of k. In this experiment, 10-fold cross validation isused for each participant following the results in [37].


100 101 102 103

MinLeafSize

0

0.2

0.4

0.6

0.8

1E

stim

ate

d o

bje

ctive

fu

nctio

n v

alu

eObjective function model

Observed pointsModel meanModel errorbarsNoise errorbarsNext pointModel minimum feasible

Fig. 4. Estimated objective function value under various minimum leafsizes.

E. Prediction performanceIn this section, comparative experiments are conducted to

evaluate the performance of the classifiers of the proposedpersonalized system. Classifiers are to build up the relationshipbetween behaviour categories and vehicle related measure-ments, so that the corresponding behaviour category can beworked out for new vehicle related measurements. In thiswork, one generic/unified framework is proposed, however,the proposed framework can automatically (i.e. without anymanual parameter retuning) generate a dedicated model foreach of the three drivers by using collected data of each driver.Considering the characteristics of the real-time application,accuracy and computation time are considered concurrently.As discussed in Section IV-A, various classifiers are comparedin this work, which include discriminant analysis based ap-proaches such as Linear Discriminant Analysis (LDA) andQuadratic Discriminant Analysis (QDA), Naive Bayes andSVM. In particular, LDA is optimized by Bayesian parameteroptimization. And the parameter setting of QDA follows [38],where δ = 0 and γ = 0. Similar to LDA, CART andNaive Bayes are also optimized using Bayesian Optimization(BO). To identify a more suitable SVM classifier, differentkernel functions are considered in this work including linear,polynomial and Gaussian kernel functions respectively. Therepresentations of linear, polynomial and Gaussian kernelfunctions are shown below

G(xi, xj) = xTi xj , (1 + xTi xj)p and e−γ||xi−xj ||2

where xi, xj denote two training samples. In polynomialkernel function, p is chosen 3 following the results in [39].In addition, following the results in [40], parameter γ = 1

2and penalty parameter C = 1 are selected. The methodto implement multi-class SVM is ‘One-vs-One’, in whichapproach K(K − 2)/2 binary classifiers are trained with Kbeing the number of classes. The final classification results arefigured out by voting through all binary classifiers, where theclass owning the most vote is selected.

To quantitatively evaluate the prediction performance, re-substitution error and cross validation (CV) error are adopted.

In particular, resubstitution error is the error for classifyingtraining dataset and CV error is the error for classifyingtesting dataset in cross validation. The comparative resultsfor three participants are shown in Tables II, respectively. Inaddition, the average resubstitution error and CV error are alsocalculated and summarized in Table III.

The following conclusions can be drawn from Tables II andIII : (1) regarding accuracy, CART+BO algorithm obtains theminimum resubstitution error and CV error for each driver,where the average resubstitution and CV error are 0.0328and 0.0371 respectively. (2) regarding computation time,discriminant analysis based approaches (e.g. LDA+BO andQDA), optimized CART and Naive Bayes+BO substantiallyoutperform SVM classifiers and are all suitable for real-timeapplication.

Considering accuracy and computation time concurrently,CART with Bayesian optimization obtains the best perfor-mance among the considered classifiers and consequentlychosen as the classifier in the proposed personalized drivingbehaviour prediction.

VI. CONCLUSIONS

This paper proposes a trajectory clustering aided person-alized driver intention prediction system for early driverintention prediction at unsignalized intersection to enhancedriving safety and efficiency. Different from some existingstudies where only manually defined manoeuvres are con-sidered using classification algorithms, this work seamlesslyintegrates unsupervised clustering and supervised classificationso that the proposed system is adaptive to individual drivers.The proposed system comprises offline training and onlineimplementation. In offline training for personalized drivingbehaviour learning, high-level driving trajectories are learntusing polynomial regression mixture clustering, leading toa set of trajectory clusters representing various driving be-haviours. Then a mapping between low-level vehicle state(e.g. speed and heading) and trajectory clusters is built usingclassification analysis. In particular, a number of classifiers arecompared, where CART with Bayesian parameter optimizationoutperforms others in terms of accuracy and computationalload and consequently chosen as the classifier in the proposedframework. In online application, the optimized CART modelis drawn to divide new samples into various trajectory clustersrepresenting different diving behaviours.

The proposed framework is validated using a recentlycollected dataset (i.e. IVSSG dataset) from real world drivingexperiments of different drivers. Regarding trajectory cluster-ing analysis, the proposed framework can provide in-depthdriving behaviour analysis than manually defined manoeuvresand is also adaptive to individual drivers. Regarding drivingbehaviour prediction, the proposed framework adopting CARTwith Bayesian parameter optimization as the classifier obtainspromising driving behaviour prediction performance in termsof resubstitution error, cross validation error and computationload.

The paper is mainly focused on developing an adaptivedriving behaviour prediction system and demonstrating its


TABLE IICLASSIFICATION PERFORMANCE COMPARISONS AMONG DIFFERENT DRIVERS

Driver 1 Driver 2 Driver 3Algorithm Resubstitution

ErrorCV Error Time

(sec./sample)ResubstitutionError

CV Error Time(sec./sample)

ResubstitutionError


LDA+BO 72.44% 72.51% 8.16E-06 55.31% 55.35% 8.25E-06 48.86% 48.93% 7.16E-06QDA 66.03% 65.96% 8.69E-06 48.41% 47.76% 1.00E-05 46.80% 46.81% 9.44E-06CART+BO 9.77% 10.98% 3.01E-05 0.05% 0.09% 9.55E-06 0.01% 0.06% 1.08E-05Naive Bayes+BO 16.34% 16.93% 1.42E-05 0.73% 0.74% 1.41E-05 0.94% 0.96% 1.22E-05SVM+Linear 66.57% 66.55% 6.06E-02 49.72% 49.68% 2.22E-02 47.85% 47.87% 1.95E-02SVM+Polynomial 48.45% 48.65% 2.27E-01 34.92% 35.02% 9.36E-02 38.10% 38.20% 1.10E-01SVM+Gaussian 44.35% 44.40% 3.15E-02 33.71% 33.90% 1.83E-02 36.95% 36.93% 1.94E-02

TABLE IIIAVERAGE PERFORMANCE FOR THREE PARTICIPANTS.

Algorithm ResubstitutionError


LDA+BO 58.87% 58.93% 7.86E-06QDA 53.74% 53.51% 9.38E-06CART+BO 3.28% 3.71% 1.68E-05Naive Bayes+BO 6.00% 6.21% 1.35E-05SVM+Linear 54.71% 54.70% 3.41E-02SVM+Polynomial 40.49% 40.62% 1.44E-01SVM+Gaussian 38.34% 38.41% 2.31E-02

feasibility using recently collected real-world experimentaldatasets. In the future, a sliding window containing a shortfeature interval will be considered to improve the robustnessof the system. Online learning will also be accommodatedinto the framework considering that drivers’ driving styleand patterns in executing various manoeuvres may changeover time. With the advent of personalized driving big data,the proposed framework can also perform abnormal drivingdetection.

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Dewei Yi (S’16) received his B.Eng. degreein 2014 in Software Engineering from ZhejiangUniversity of Technology, Zhejiang, China. In2015, he obtained his M.Sc. degree with Distinc-tion from the Department of Computer Science,Loughborough University, Loughborough, U.K.In 2018, received a Ph.D degree in the Depart-ment of Aeronautical and Automotive Engineer-ing, Loughborough University, Loughborough,U.K. Since 2018, he has been a postdoctoralresearch associate in Centre for Autonomous

Systems at Loughborough University.His current research interests include personalized driving assistance,

autonomous vehicle, vehicular network and Advanced Driver AssistanceSystems (ADASs). Dr Yi is under the grant of China Scholarship Council.In 2015, he received CommAgility MSc Project Prize for best wirelesscommunication project.

Jinya Su (M’16) received his B.Sc. degree inthe School of Mathematics and Statistics fromShandong University, Weihai, China in 2011. In2016, he received a Ph.D degree in the De-partment of Aeronautical and Automotive En-gineering, Loughborough University, Loughbor-ough, U.K. Since 2015, he has been a researchassociate in Centre for Autonomous Systems atLoughborough University.

His research interests include Kalman filter,machine learning and their applications to au-

tonomous systems such as intelligent vehicle, agricultural informationsystem.

Dr Su received the Best Student Paper Award in 19th InternationalConference on Automation and Computing (2013), the IEEE-IES Stu-dent Paper Travel Award in 17th International Conference on IndustrialTechnology (2016), and the Annual ICI Prize from the Institute ofMeasurement and Control in 2016. In 2015, he received the prestigiousChinese Government Award for Outstanding Self-financed StudentsAbroad.

Cunjia Liu (M’16) received his B.Eng. and M.Sc.degrees in guidance, navigation, and controlfrom Beihang University, Beijing, China, in 2005and 2008, respectively. In 2011, he receiveda Ph.D. degree in autonomous vehicle controlfrom Loughborough University, Loughborough,United Kingdom. From 2011, he was a researchassociate with the Department of Aeronauti-cal and Automotive Engineering at Loughbor-ough University, where he was appointed as aLecturer in flight dynamics and control, or un-

manned vehicles in 2013 and Senior Lecturer in 2018.His current research interests include optimization-based control,

disturbance-observer based control, Bayesian information fusion andtheir applications to autonomous vehicles for flight control, path plan-ning, decision making, and situation awareness.

Wen-Hua Chen (M’00–SM’06–F’17) receivedthe M.Sc. and Ph.D. degrees from NortheastUniversity, Shenyang, China, in 1989 and 1991,respectively. From 1991 to 1996, he was aLecturer and then Associate Professor with theDepartment of Automatic Control, Nanjing Uni-versity of Aeronautics and Astronautics, Nanjing,China. From 1997 to 2000, he held a researchposition and then a Lecturer in control engineer-ing with the Centre for Systems and Control, Uni-versity of Glasgow, Glasgow, U.K. In 2000, he

moved to the Department of Aeronautical and Automotive Engineering,Loughborough University, Loughborough, U.K., as a Lecturer, where hewas appointed as a Professor in 2012.

His research interests include the development of advanced control,signal processing and decision making methods and their applicationsin aerospace engineering. As a professor in Autonomous Vehicles, he isCurrently mainly working on the development of unmanned autonomoussystems.

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